Smoothed Analysis of Algorithms: Why the Simplex Algorithm Usually Takes Polynomial Time
Data Structures and Algorithms
2009-09-25 v7
Abstract
We introduce the smoothed analysis of algorithms, which is a hybrid of the worst-case and average-case analysis of algorithms. In smoothed analysis, we measure the maximum over inputs of the expected performance of an algorithm under small random perturbations of that input. We measure this performance in terms of both the input size and the magnitude of the perturbations. We show that the simplex algorithm has polynomial smoothed complexity.
Cite
@article{arxiv.cs/0111050,
title = {Smoothed Analysis of Algorithms: Why the Simplex Algorithm Usually Takes Polynomial Time},
author = {Daniel A. Spielman and Shang-Hua Teng},
journal= {arXiv preprint arXiv:cs/0111050},
year = {2009}
}
Comments
Revised. Improved statement of main theorem